nthroot.c 文件参考

#include <math.h>
#include "../../../include/lammp/numth.h"

nthroot.c 的引用(Include)关系图:

浏览源代码.

函数
ulong	lmmp_nthroot_ulong_ (ulong n, ulong root)
	计算 floor(n^(1/root))
ulong	lmmp_sqrt_ulong_ (ulong a)
	Copyright (C) 2026 HJimmyK(Jericho Knox)
static ulong	pow_n (ulong x, ulong n)

变量
static const float	inv_table []
static const uint16_t	max_base []

函数说明

lmmp_nthroot_ulong_()

ulong lmmp_nthroot_ulong_	(	ulong	n,
		ulong	root
	)

计算 floor(n^(1/root))

参数

n	被开方数
root	开方次数

返回

floor(n^(1/root))

注解

root=0时，返回0

在文件 nthroot.c 第 55 行定义.

                                               {
    ulong x, currval, base, upper_limit;
 
    if (n == 0 || root == 0)
        return 0;
    if (root == 1)
        return n;
    if (root == 2)
        return lmmp_sqrt_ulong_(n);
    if (root == 3)
        return lmmp_cbrt_ulong_(n);
 
    if (root >= LIMB_BITS || n < (1ULL << root))
        return 1;
 
    /* n <= upper_limit^root */
    upper_limit = max_base[root - 4];
 
    if (upper_limit == 2)
        return upper_limit;
 
    /* upper_limit = 2 for root >= 41 */
    lmmp_debug_assert(root <= 40);
 
    if (root == 4)
        x = sqrt(sqrt(n));
    else
        x = expf(inv_table[root - 5] * logf(n));
 
    base = x;
 
    if (base >= upper_limit)
        base = upper_limit - 1;
 
    currval = pow_n(base, root);
    if (currval == n)
        return base;
 
    while (currval <= n) {
        base++;
        currval = pow_n(base, root);
        if (base == upper_limit)
            break;
    }
 
    while (currval > n) {
        base--;
        currval = pow_n(base, root);
    }
 
    return base;
}

引用了 inv_table, LIMB_BITS, lmmp_cbrt_ulong_(), lmmp_debug_assert, lmmp_sqrt_ulong_(), max_base, n , 以及 pow_n().

函数调用图:

lmmp_sqrt_ulong_()

ulong lmmp_sqrt_ulong_

(

ulong

a

)

Copyright (C) 2026 HJimmyK(Jericho Knox)

计算算术平方根 floor(sqrt(a))

This file is part of LAMMP.

LAMMP is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed WITHOUT ANY WARRANTY.

See https://www.gnu.org/licenses/.

在文件 nthroot.c 第 21 行定义.

                                {
    ulong is;
 
    is = (ulong)sqrt((double)a);
 
    is -= (is * is > a);
    if (is == (1ULL << 32))
        is--;
    return is;
}

引用了 n.

被这些函数引用 lmmp_nthroot_ulong_().

这是这个函数的调用关系图:

pow_n()

static ulong pow_n ( ulong  x, ulong  n  )

inlinestatic

在文件 nthroot.c 第 32 行定义.

                                            {
    ulong ret = 1;
    for (ulong i = 0; i < n; ++i) {
        ret *= x;
    }
    return ret;
}

引用了 n.

被这些函数引用 lmmp_nthroot_ulong_().

这是这个函数的调用关系图:

变量说明

inv_table

const float inv_table[]

static

初始值:

= {
    0.200000000000000, 0.166666666666667, 0.142857142857143, 0.125000000000000, 0.111111111111111, 0.100000000000000,
    0.090909090909091, 0.083333333333333, 0.076923076923077, 0.071428571428571, 0.066666666666667, 0.062500000000000,
    0.058823529411765, 0.055555555555556, 0.052631578947368, 0.050000000000000, 0.047619047619048, 0.045454545454545,
    0.043478260869565, 0.041666666666667, 0.040000000000000, 0.038461538461538, 0.037037037037037, 0.035714285714286,
    0.034482758620690, 0.033333333333333, 0.032258064516129, 0.031250000000000, 0.030303030303030, 0.029411764705882,
    0.028571428571429, 0.027777777777778, 0.027027027027027, 0.026315789473684, 0.025641025641026, 0.025000000000000,
}

在文件 nthroot.c 第 40 行定义.

                                 {
    0.200000000000000, 0.166666666666667, 0.142857142857143, 0.125000000000000, 0.111111111111111, 0.100000000000000,
    0.090909090909091, 0.083333333333333, 0.076923076923077, 0.071428571428571, 0.066666666666667, 0.062500000000000,
    0.058823529411765, 0.055555555555556, 0.052631578947368, 0.050000000000000, 0.047619047619048, 0.045454545454545,
    0.043478260869565, 0.041666666666667, 0.040000000000000, 0.038461538461538, 0.037037037037037, 0.035714285714286,
    0.034482758620690, 0.033333333333333, 0.032258064516129, 0.031250000000000, 0.030303030303030, 0.029411764705882,
    0.028571428571429, 0.027777777777778, 0.027027027027027, 0.026315789473684, 0.025641025641026, 0.025000000000000,
};

被这些函数引用 lmmp_nthroot_ulong_().

max_base

const uint16_t max_base[]

static

初始值:

= {
    65535, 7131, 1625, 565, 255, 138, 84, 56, 40, 30, 23, 19, 15, 13, 11, 10, 9, 8, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3,
    3,     3,    3,    3,   3,   3,   3,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

在文件 nthroot.c 第 51 行定义.

                                   {
    65535, 7131, 1625, 565, 255, 138, 84, 56, 40, 30, 23, 19, 15, 13, 11, 10, 9, 8, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3,
    3,     3,    3,    3,   3,   3,   3,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2};

被这些函数引用 lmmp_nthroot_ulong_().